How to survive in a black hole: Myth Debunked

Published online: 18 May 2007; | doi:10.1038/news070514-21
How to survive in a black hole
There's no escape, but how can you maximize your remaining time?
Philip Ball

Aaaaaaaaaaargh: how to draw out your torturous fall into a black hole.

NASA

So there you are: you discover that your spaceship has inadvertently slipped across the event horizon of a black hole — the boundary beyond which nothing, not even light, can escape the hole's fearsome gravity. The only question is how you can maximize the time you have left. What do you do?

A common idea in physics is that you shouldn't try to blast your way out of there. Black holes, it's said, are like the popular view of quicksand: the harder you struggle, the worse things become.

But Geraint Lewis and Juliana Kwan of the University of Sydney in Australia say this is a myth. Their analysis of the problem, soon to be published in the Proceedings of the Astronomical Society of Australia1, shows that in general your best bet is indeed to turn on the rocket's engine. You'll never escape, but you'll live a little longer.

Falling into a black hole is a strange affair. Because the hole's gravity distorts space-time, a far-off observer watching an object crossing the event horizon sees time for that object appear to slow down — a clock falling into a black hole would appear, from the outside, to tick ever slower. At the horizon itself, time stops, and the object stays frozen there for the remaining lifetime of the Universe.

But this isn't how things seem to the in-falling object itself. Indeed, if the black hole is big enough, nothing noticeable happens when a spaceship crosses its event horizon — you could stray inside without realizing. Yet once inside, nothing can save you from being crushed by the hole's gravity sooner or later.

Live long and prosper

Clearly, an astronaut in that situation might prefer it to be later. For a supermassive black hole such as that thought to exist at the Galactic Centre, the survival time could be hours. To stretch it out for as long as possible, the astronaut might be tempted to turn on rocket thrusters and try to head outwards, away from the hole's fatal 'singularity' at the centre.

But best not to, according to some sources. An article on black holes on the cosmology website of the University of California, Berkeley, for example, says "the harder you fire your rockets, the sooner you hit the singularity. It's best just to sit back and enjoy the ride."

Lewis and Kwan say this is mistaken. They point out that the analysis is usually done by thinking about a person who falls into the black hole starting from a state of rest at the event horizon. In that case, it's true that accelerating away from the singularity by using the rocket thrusters will only speed your demise. The longest survival time possible in that instance is free fall. Because all paths lead inevitably to the singularity, trying to travel faster - in any direction - only takes you there quicker.

Long and winding road

But in general a person falling past the horizon won't have zero velocity to begin with. Then the situation is different — in fact it's worse. So firing the rocket for a short time can push the astronaut back on to the best-case scenario: the trajectory followed by free fall from rest.

"There is one longest road - the freefall road starting from rest - as well as many shorter roads," Lewis explains. "If you cross the event horizon on one of the shorter roads, you can fire your rocket to move you on to the longest road."

But this has to be done judiciously. "If you overdo it, you will overshoot the longest road and end up on a shorter road on the other side," says Lewis. So you only want to burn your rocket for a certain amount of time, and then turn it off. "Once you know how fast you have passed through the event horizon, it is reasonably straightforward to calculate how long you need to burn your rocket to get on to the best path," he says. "The more powerful the rocket, the quicker you get on to this path." Starship captains, take note.

There's nothing particularly surprising in this analysis, but black-hole experts say that debunking this common misconception could have an educational value. "It's a misconception I had when I first did relativity many years ago, and one which I have heard in discussions with others," says Lewis. "It has generated a substantial discussion on the Wikipedia entry about black holes."

He adds that "even Einstein had a very hard time attempting to fathom just what is going on as things fall into a black hole."

From time to time, people ask if I've ever spotted any errors in MTW, which was published way back in 1973 and remains a standard resource for students of gtr, which good reason. Compare Exercise 31.4 in MTW with http://www.arxiv.org/abs/0705.1029, the eprint which the Nature article is referring to, which purports to correct an overly ambitious statement in the exercise. (The point made by Lewis and Kwan is that the argument suggested by MTW only applies assuming certain boundary conditions on the motion of the infalling observers.)

"It has generated a substantial discussion on the Wikipedia entry about black holes."

That does ring a faint bell. Presumably, this "substantial discussion" would be somewhere in one of the archives of http://en.wikipedia.org/wiki/Talk:Black_hole but I can't find it. Anyone know what discussion Lewis was referring to?

A free falling (Lemaître) observer maximizes his proper time between infinity and the singularity.

As soon as an observer momentarily diverges from free falling he is going to accumulate less proper time compared to an observer who did not accelerate. In the case of an observer who is accelerating away from the black hole when he crosses the event horizon, the best that he can do is to make the accelerated time interval as short as possible by accelerating in the opposite direction until his prior acceleration is neutralized. But the "lost time" between the accelerations is unrecoverable.

With respect to these situations it is interesting to take a look at the Gullstrand-Painlevé coordinate chart of the Schwarzschild metric. It describes a flat background (not to be confused with the metric) and uses a so-called shift vector (as in the ADM formalism) representing the gravitational pull. With this chart it is much easier to separate the Lorentzian effects from the gravitational effects, and an extra plus is that the shift vector behaves in a Galilean as opposed to a Lorentzian fashion. Another advantage is that the chart maps both the external and internal regions of the black hole.

In Minkowski spacetime we can see the same kind of effects on proper time as in the case of the black hole with regards to acceleration, for instance in the twin thought experiment. Two twins A and B are free falling in spacetime, A accelerates away from B. From that moment on, A is going to accumulate less proper time than B. Close to his point of return A accelerates towards B until they again are at rest with each other. From that moment on, A and B are going to accumulate the same amount of proper time.

But as soon as A returns by accelerating towards B, A again is going to accumulate less proper time than B. And finally, when A is very close to B, A accelerates away from B until A and B are again at rest with each other. From that moment on, A and B are going to accumulate exactly the same amount of proper time. But A´s "lost time" between the accelerations is unrecoverable.

It is possible that in some curved spacetimes an observer can actually accumulate more proper time between two events by performing at least two carefully planned accelerations. This is the case if he is going to travel along a geodesic that is a local, but not a global maximum. If he manages to travel to, and then free fall along the global maximum geodesic then he could, in principle, record more proper time than if he would have ridden along the shorter geodesic. But this is definitly not possible in case of a spacetime with a Minkowski or Schwarzschild metric.

From time to time, people ask if I've ever spotted any errors in MTW, which was published way back in 1973 and remains a standard resource for students of gtr, which good reason. Compare Exercise 31.4 in MTW with http://www.arxiv.org/abs/0705.1029, the eprint which the Nature article is referring to, which purports to correct an overly ambitious statement in the exercise. (The point made by Lewis and Kwan is that the argument suggested by MTW only applies assuming certain boundary conditions on the motion of the infalling observers.)

Exercise 31.4 in MTW, including the boundary condition given in its hint, is completely consistent with the eprint.

May I ask why you reverted my edit? The information I posted was perfectly correct. It is a well known fact of General Relativity that geodesics are paths of maximal proper time. --Jpowell 09:30, 1 March 2006 (UTC)

On my talk page you said:

"Let's say you and I are on two different rocket ships approaching a galactic black hole. After crossing the event horizon you accelerate away from the black hole, while I accelerate toward the black hole. Obviously my rocket ship is going to disintegrate first.

What you wrote may be correct under certain technical sense, but read contradictory to the general audience. -MegaHasher 17:45, 1 March 2006 (UTC)"

That is not what I said. I was saying that once you fall into a black hole it is better to turn your engine off and simply fall into the singularity if you want to survive for longer. Accelerating in any direction will hasten your demise. It is not wise to talk about what is obvious in a region of very highly curved spacetime, a lot of very weird effects come into play.

"General Relativity tells us that once past the event horizon an object will always move closer to the singularity. A consequence of this is that a pilot in a powerful rocket ship that had just crossed the event horizon who tried to accelerate away from the singularity would actually fall in faster. As the ship tried to move faster time dilation would mean the inevitable fall into the singularity would simply occur faster, or as an alternative way of viewing the situation, length contraction would bring the singularity closer to the ship. This is related to the fact that geodesics (or unaccelerated trajectories) are also paths of maximal proper time."

I would like to reinstate this, but don't want to get into an edit war with you, if you could suggest a rewording or a part that needs clarification that would be appreciated.

[edit] Black Hole Discussion mk2

"IMHO, only the first sentence of the paragraph is true; the last sentence may be true, but since the object is accelerating, may not be applicable. A possible revision may be "General Relativity tells us that once past the event horizon an object will always move closer to the singularity. A consequence of this is that a pilot in a powerful rocket ship that had just crossed the event horizon cannot avoid its eventual destruction by firing its rocket."

I'm currently studying General Relativity at university and am confident that all parts of the statement are true. It is the acceleration that causes the worldline of the pilot to diverge from a geodesic (geodesics are unaccelerated trajectories), hence a deviation from longest possible proper time.

Simply stating the point that you cannot avoid destruction is pointless as this is a very basic consequence of passing the event horizon. It is more physically interesting that acceleration speeds up your doom, think of the analogy of struggling against quicksand, you will simply be pulled in faster.

Anyway, statements like that already appear multiple times in the black hole topic. I have started an effort to trim the article toward 32k in size; if you can help me in that, it would be great. For example, look for similar statements that were raised multiple times, long winded technical mumbo jumbo, or multiple explainations for a single term. -MegaHasher 20:48, 1 March 2006 (UTC)

That is not what I said. I was saying that once you fall into a black hole it is better to turn your engine off and simply fall into the singularity if you want to survive for longer. Accelerating in any direction will hasten your demise.

This isn't correct. In fact, this is the mythconception (paper's term) debunked by the paper for which Chris has given a link in post #2.

For an astronaut that falls through the event horizon with a non-zero velocity relative to an observer "at rest" at (i.e., infinitesimally close to) the event horizon, the best course of action is to fire his rocket inside the event horizon.

You have to remember that time near to black holes slows down, so you would move a lot slower than you normally would.

This is what an observer outside sees, which isn't relevant here. This thread is about time as measured on the watch of someone who falls into the black hole.

Anyway, how do people know that they will die?

A person falls feet-first into a black experiences a tidal force that pulls his body apart. In terms of Newtonian gravity, the person's feet are closer to the object than his head, thus the feet experience more gravitational pull than the head. Ouch!

As an analogy, suppose that you are suspended with hands over your head by a (strong) rope tied about your wrists. A dangling rope is tied about your ankles, and more and more weight is added to this bottom rope. Eventually your body pulls apart.

May I ask why you reverted my edit? The information I posted was perfectly correct. It is a well known fact of General Relativity that geodesics are paths of maximal proper time. --Jpowell 09:30, 1 March 2006 (UTC) ....

Cusp, I don't really understand the point of your post. It appears that you have come here to ask why someone has changed what you have written on wikipedia, which seems a strange thing to do. Especially, since you are clearly talking directly to someone, but have not said to whom you are talking! At a guess, I'd say it was aimed at Chris, but only as I know he used to write on wikipedia.

Anyway, I suggest you take such a discussion back to wikipedia, as this is not the correct place for it.

I think what happened is that the discussion on the wikipedia was mentioned earlier in this thread, so it was simply quoted. A little bit of editing would have made it clearer that the discussion wasn't being reopened, just that the old discussion was being quoted because a question was asked about it specifically.

Cusp: I agree with everything you said (including the self-critique!), but I am not sure you found the discussion referred to in the Nature item, since these two posters seem to be arguing over something different from the (oversimplified) remark in Carroll.

"General Relativity tells us that once past the event horizon an object will always move closer to the singularity. A consequence of this is that a pilot in a powerful rocket ship that had just crossed the event horizon who tried to accelerate away from the singularity would actually fall in faster. As the ship tried to move faster time dilation would mean the inevitable fall into the singularity would simply occur faster, or as an alternative way of viewing the situation, length contraction would bring the singularity closer to the ship. This is related to the fact that geodesics (or unaccelerated trajectories) are also paths of maximal proper time."

I think this text, taken from the wikipedia discussion above, *is* essentially the essentially the "no struggle" view point. I guess it's just part of the discussion.

A consequence of this is that a pilot in a powerful rocket ship that had just crossed the event horizon who tried to accelerate away from the singularity would actually fall in faster.

J. Powell then queried why MegaHasher had removed this material (of which the above statement is only a part), and stated at User talk:MegaHasher that he wished to reinsert it. In his reply, MegaHasher did not mention the statement I quoted. IOW, as I stated, their discussion seems to have concerned something else.

Recall that the Nature on-line article stated:

"It's a misconception I had when I first did relativity many years ago, and one which I have heard in discussions with others," says Lewis. "It has generated a substantial discussion on the Wikipedia entry about black holes."

My question is: does anyone know where is this "substantial discussion"?

I would guess what it meant is that disussions of this sort have taken place on the internet (including wikipedia), rather than only wikipedia, and that it was written on the run without expecting to be directly quoted.

I would guess what it meant is that disussions of this sort have taken place on the internet (including wikipedia), rather than only wikipedia, and that it was written on the run without expecting to be directly quoted.

Cusp == Geraint

OK, check, thanks for clearing up both my spoken and unspoken questions! And welcome to PF, hope you stick around.